Biometrics is commonly used to identify and/or authenticate users on the basis of individual physical characteristics.
Such an identification using biometrics, implemented by a biometric authentication system, comprises the following three main steps:                capturing a reference biometric sample coming from the authorized user (for example a reference image of an authorized user);        creating a reference file or  reference signature (which includes at least one characteristic element of the reference image) by means of a specific processing operation applied to the reference biometric sample, and then storing this reference file;        carrying out a verification wherein, just as in the above capturing and creating steps, a biometric sample to be compared coming from the user to be authenticated is captured and a file to be compared or  signature to be compared is created and then the reference file is compared with the file to be compared to determine their rate of similitude and to take the requisite decision.        
Thus, the stored pieces of information are not biometric samples but mathematical models of these samples which distinguish one biometric sample from another. This model is called a  signature or a  template.
The creation of a reference signature is done during a phase known as an enrolment (or learning) phase which groups together the steps for capturing the reference biometric sample, creating and storing the reference signature and storing pieces of information on the user's identity such as his family name, forename, identifier (personal identification number).
The authentication of a user by biometrics can be based especially on the measurement (or capture) of at least one of the following biometric samples, or a combination of one or more of the following biometric samples:                his fingerprint;        his palm print (hand print);        his retinal print;        his iris print;        his face print (the shape of the face).        
One drawback of these prior art biometric authentication systems lies in their slowness when they are used to reference a large number of users (for example to control access to an urban rail network in major urban agglomeration or to authenticate a user of a bank card).
Indeed, the duration of the verification step during which the authentication decision proper is taken depends on the number of users referenced in the authentication system. The greater the number of users, the greater is the number of potential comparisons to be made to determine or not determine the authentication of a user.
Thus, the greater the number of users, the slower is the system. Furthermore, the increase in the number of users tends to increase the probability of collision between biometric data and hence reduce the general reliability of the system (this is the phenomenon known in the prior art as the  false positive(s) phenomenon).
One corollary of this latter drawback is that it is difficult to implement a method of payment by means of biometric data. Indeed, to make it possible to set up such a method of payment, it is necessary to compare the user's biometric data with a large number of pieces of biometric data pertaining to other users, pieces of data that very probably belong to financial establishments and which could prove to be very complicated to obtain. Now, as a matter of principle, a user should not disclose information about his bank, and the comparison of the user's biometric data should be done on all the pieces of data recorded in the authentication system.